To explore the full potential of Quantum-inspired Evolutionary Algorithms (QEA) in multiobjective design optimizations, a vector QEA is proposed. To fulfill the two ultimate goals of a vector optimizer in finding and uniformly sampling the Pareto front of a multi-objective inverse problem, a fitness assignment formula to consider the number of improvements in the whole objective functions and the amount of the improvement in a specified objective function, as well as the use of a selection mechanism in choosing the so far searched best solutions, are proposed in this paper. The information sharing and the increment angle updating components of the scalar QEA have also been redesigned according to the characteristics of multi-objective inverse problems. Numerical results on two case studies are presented to validate the proposed vector QEA.